CN108333935B - Precise debugging method and system based on second-order notch filter - Google Patents

Precise debugging method and system based on second-order notch filter Download PDF

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CN108333935B
CN108333935B CN201810086329.2A CN201810086329A CN108333935B CN 108333935 B CN108333935 B CN 108333935B CN 201810086329 A CN201810086329 A CN 201810086329A CN 108333935 B CN108333935 B CN 108333935B
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notch filter
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冯伟
冀娟
曾凡铨
胡翔宇
王尧尧
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Shanghai Aerospace Control Technology Institute
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Abstract

A precise debugging method and a system based on a second-order notch filter are characterized in that an initial frequency characteristic of a debugging object is obtained by performing mathematical simulation or frequency sweep test on the debugging object, a resonant frequency, a resonant peak value and a frequency range needing to be corrected of the debugging object are obtained accordingly, a notch central frequency, a notch depth and a notch bandwidth of the second-order notch filter are determined according to the information, the three information quantities are used as input, a numerator damping coefficient and a denominator damping coefficient of the second-order notch filter are calculated, and a precise mathematical model of the second-order notch filter is finally established, so that the debugging object can be debugged. In the debugging process, if the frequency characteristic of a debugging object is different from the index requirement, the notch depth and the notch bandwidth can be properly adjusted according to the difference condition to gradually reach the index requirement, the next debugging can be conducted in a guiding manner according to the last debugging result in the debugging process, and the debugging efficiency is greatly improved while the accurate debugging is realized.

Description

Precise debugging method and system based on second-order notch filter
Technical Field
The invention relates to a precise debugging method and system based on a second-order notch filter, and relates to the field of automatic control.
Background
The notch filter is a common means for improving the resonance characteristics of a servo control system or the like, and is most widely cited as a quadratic notch filter, whose mathematical model n(s) is as shown in the following equation (4), and whose output characteristics are shown in fig. 1. Design parameters for a second order notch filter include notch center frequency ω0And notch damping coefficient ξ1、ξ2Trap central frequency omega0Can be determined according to simulation or sweep frequency test results, andnotch damping coefficient xi1、ξ2At present, no scientific determination method exists, and the conventional method is trial and error according to xi1、ξ2And influence rules are explored due to different values. The method can not intuitively, quantitatively and regularly obtain xi1、ξ2Such as the notch depth D, notch bandwidth B, etc., on the quadratic notch filter. Therefore, the debugging method cannot realize accurate debugging of the debugging object, and is poor in debugging regularity and guidance and low in debugging efficiency.
Disclosure of Invention
The technical problem solved by the invention is as follows: the defects of the prior art are overcome, and the accurate debugging method and the accurate debugging system based on the second-order notch filter are provided, so that the expected notch central frequency omega can be determined only according to the initial frequency characteristic of a debugging object0The notch depth D and the notch bandwidth B, and then an accurate mathematical model (namely a transfer function) of the second-order notch filter can be established, so that accurate debugging of a debugging object is realized.
The technical scheme of the invention is as follows: a precise debugging method based on a quadratic notch filter comprises the following steps:
(1) resonance frequency of tuning object according to quadratic notch filter and frequency range to be corrected (i.e., start frequency ω)1To the end frequency omega2Range of (d) determining a notch center frequency ω of the quadratic notch filter0Start frequency omega1End frequency omega2；
(2) Determining a notch depth D of the second-order notch filter according to a resonance peak value of a debugging object of the second-order notch filter;
(3) according to the starting frequency omega1End frequency omega2Determining a notch bandwidth B of a quadratic notch filter;
(4) notching central frequency point omega according to the step (1)0Calculating a notch depth D of the step (2) and a notch bandwidth B of the step (3), and calculating a molecular damping coefficient xi of the quadratic notch filter1And denominator damping coefficient xi2；
(5) According to step (1)Trapped wave center frequency point omega0And (4) the molecular damping coefficient xi of the second order notch filter of the step (4)1And denominator damping coefficient xi2Establishing a mathematical model of a second-order notch filter;
(6) debugging the frequency characteristic of the debugging object according to the mathematical model obtained in the step (5);
(7) and (4) confirming the debugging result in the step (6), if the debugging result is different from the index requirement, properly adjusting the notch depth D and the notch bandwidth B according to the difference condition, repeating the steps (4), (5) and (6), and establishing a new mathematical model of the second-order notch filter for debugging again until the index requirement is met. The influence of the notch depth D and the notch bandwidth B on the debugging object is as follows: the deeper the notch depth D, the smaller the amplitude at the notch center frequency, but the higher the amplitude before the notch center frequency, while the wider the notch width B, the more the amplitude before the notch center frequency is affected.
In the step (2), the depth D of the trapped wave is required to be below-3 dB, and the molecular damping coefficient xi1And denominator damping coefficient xi2The method is effective.
In the step (3), according to the starting frequency omega1End frequency omega2Determining the bandwidth B of the quadratic notch filter, wherein the formula is as follows:
B＝|ω2-ω1| (1)。
step (4) according to the notch central frequency point omega of the step (1)0Determining the notch depth D of the step (2) and the bandwidth B of the step (3) and determining the molecular damping coefficient xi of the quadratic notch filter1The formula is as follows:
Figure GDA0003270924860000021
step (4) according to the notch central frequency point omega of the step (1)0Determining a denominator damping coefficient xi of a quadratic notch filter according to the notch depth D in the step (2) and the notch bandwidth B in the step (3)2The formula is as follows:
Figure GDA0003270924860000031
the mathematical model n(s) of the quadratic notch filter of step (5) is as follows:
Figure GDA0003270924860000032
determining a trapped wave center frequency point omega of a second-order trapped wave filter according to the resonant frequency of a debugging object of the second-order trapped wave filter and a frequency range to be corrected0Start frequency omega1End frequency omega2The method is obtained by adopting mathematical simulation or frequency sweep test.
The invention discloses a precise debugging system based on a quadratic notch filter, which comprises: the device comprises a frequency determining module, a trapped wave depth determining module, a trapped wave bandwidth determining module, a damping coefficient determining module, a modeling module and a debugging module;
a frequency determining module for determining the notch central frequency omega of the second order notch filter according to the resonant frequency of the debugging object of the second order notch filter and the frequency range to be corrected0Start frequency omega1End frequency omega2；
The trapped wave depth determining module is used for determining the trapped wave depth D of the second-order trapped wave filter according to the resonance peak value of the debugging object of the second-order trapped wave filter;
a notch bandwidth determination module for determining the notch bandwidth based on the start frequency ω1End frequency omega2Determining a notch bandwidth B of a quadratic notch filter;
a damping coefficient determining module for determining the notch center frequency point omega according to the frequency0The notch depth D determined by the notch depth determining module and the notch bandwidth B determined by the notch bandwidth determining module, and calculating the molecular damping coefficient xi of the quadratic notch filter1And denominator damping coefficient xi2；
A modeling module for determining the notch center frequency point omega according to the frequency0Molecular damping of a quadratic notch filter of a damping coefficient determination moduleCoefficient xi1And denominator damping coefficient xi2Establishing a mathematical model of a second-order notch filter;
and the debugging module is used for debugging the frequency characteristic of the debugging object according to the mathematical model obtained by the modeling module to obtain a debugging result.
Compared with the prior art, the invention has the advantages that:
(1) the invention can obtain the characteristic parameters (notch central frequency omega) of the ideal second-order notch filter in advance0The notch depth D and the notch bandwidth B) to further determine an accurate second-order notch filter mathematical model, and the debugging effect of the second-order notch filter can be better consistent with the expected effect, and the debugging accuracy is high;
(2) according to the frequency characteristic of a debugging object, the expected characteristic of the second-order notch filter is determined, then the mathematical model of the second-order notch filter is established for debugging, namely the actual result is debugged by directly using the obtained 'ideal result', and the debugging efficiency is greatly improved;
(3) the characteristics of the second-order notch filter can be obtained in advance, if the debugging result deviates from the index requirement in the debugging process, the corresponding characteristic parameters (notch depth D and notch bandwidth B) of the second-order notch filter can be adjusted clearly according to the debugging result, and the debugging regularity is strong and the guidance quality is good;
(4) the invention provides a molecular damping coefficient xi of a second-order notch filter1And denominator damping coefficient xi2The precise calculation method of (2);
(5) the invention determines a flow chart of a debugging method based on a quadratic notch filter.
Drawings
FIG. 1 is a graph of the amplitude-frequency characteristics of a second order notch filter of the present invention;
FIG. 2 is a block diagram of the electromechanical servo system;
FIG. 3 is a graph of an initial frequency characteristic of the electromechanical servo system;
fig. 4 is a graph of the frequency characteristics of the electromechanical servo system after final debugging is completed.
FIG. 5 is a flowchart of a debugging method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
The invention discloses a precise debugging method and a precise debugging system based on a second-order notch filter, which are used for realizing precise debugging of the frequency characteristic of a debugging object. The initial frequency characteristic of the debugging object is obtained by performing mathematical simulation or frequency sweep test on the debugging object, and accordingly, the resonant frequency, the resonant peak value and the frequency range needing to be corrected (namely, the initial frequency and the end frequency are determined) of the debugging object are obtained. According to the information, determining the notch center frequency (same as the resonance frequency), the notch depth and the notch bandwidth of the quadratic notch filter, taking the three information quantities as input, calculating the numerator damping coefficient and the denominator damping coefficient of the quadratic notch filter, and finally establishing an accurate mathematical model (namely a transfer function) of the quadratic notch filter, namely debugging the object. In the debugging process, if the frequency characteristic of the debugging object is still different from the index requirement, the notch depth and the notch bandwidth can be properly adjusted according to the difference condition, and the index requirement is gradually met. The method discards the defects of poor precision, low efficiency, regularity and poor guidance quality of the conventional parameter trial-and-error debugging method, and provides a scientific debugging method for establishing the accurate mathematical model of the second-order notch filter.
The invention provides a scientific debugging method for establishing an accurate mathematical model of a notch filter, which avoids the defects of poor precision, low efficiency, regularity and poor guidance of the conventional parameter trial-and-error debugging method, can be used for carrying out next debugging in a guiding manner according to the last debugging result in the debugging process, and greatly improves the debugging efficiency while realizing accurate debugging. The debugging flow of the present invention is shown in fig. 5.
The invention discloses a precise debugging system based on a quadratic notch filter, which is characterized by comprising the following components: the device comprises a frequency determining module, a trapped wave depth determining module, a trapped wave bandwidth determining module, a damping coefficient determining module, a modeling module and a debugging module;
a frequency determining module for determining the notch central frequency omega of the second order notch filter according to the resonant frequency of the debugging object of the second order notch filter and the frequency range to be corrected0Start frequency omega1End frequency omega2；
The trapped wave depth determining module is used for determining the trapped wave depth D of the second-order trapped wave filter according to the resonance peak value of the debugging object of the second-order trapped wave filter;
a notch bandwidth determination module for determining the notch bandwidth based on the start frequency ω1End frequency omega2Determining a notch bandwidth B of a quadratic notch filter; the characteristics of the second-order notch filter can be obtained in advance, if the debugging result deviates from the index requirement in the debugging process, the corresponding characteristic parameters (notch depth D and notch bandwidth B) of the second-order notch filter can be adjusted clearly according to the debugging result, and the debugging regularity is strong and the guidance quality is good.
A damping coefficient determining module for determining the notch center frequency point omega according to the frequency0The notch depth D determined by the notch depth determining module and the notch bandwidth B determined by the notch bandwidth determining module, and calculating the molecular damping coefficient xi of the quadratic notch filter1And denominator damping coefficient xi2；
A modeling module for determining the notch center frequency point omega according to the frequency0And the molecular damping coefficient xi of the second-order notch filter of the damping coefficient determination module1And denominator damping coefficient xi2Establishing a mathematical model of a second-order notch filter; the invention can obtain the characteristic parameters (notch central frequency omega) of the ideal second-order notch filter in advance0The notch depth D and the notch bandwidth B) to further determine an accurate second-order notch filter mathematical model, and the debugging effect of the second-order notch filter can be better consistent with the expected effect, and the debugging accuracy is high; according to the frequency characteristic of the debugging object, the expected characteristic of the quadratic notch filter is determined, and then the mathematical model of the quadratic notch filter is established for debugging, namely, the obtained 'ideal result' is directly usedThe actual result is debugged, and the debugging efficiency is greatly improved.
And the debugging module is used for debugging the frequency characteristic of the debugging object according to the mathematical model obtained by the modeling module to obtain a debugging result.
The specific implementation will be described by taking the frequency characteristic adjustment of the electromechanical servo system for controlling the inertia load swing as an example.
The electromechanical servo system is a position follow-up system for controlling the swinging of certain inertia load, and comprises a servo controller, a servo motor, a speed reducer, a position sensor and the like, and the system composition block diagram is shown in figure 1. The servo controller receives a swing angle instruction of the upper computer, collects swing angle feedback information of the position sensor in real time, performs comprehensive operation to obtain control output, drives the servo motor to operate, and drives the load to swing according to the given swing angle instruction through torque amplification and rotating speed adjustment of the speed reducer.
Before debugging, the initial frequency characteristic of the position servo system needs to be obtained in advance, and as shown in fig. 3, the initial frequency characteristic curve of the electromechanical servo system can be obtained through mathematical simulation or frequency sweep test. In general, a mathematical simulation model of a position servo system is built by using a MATLAB tool, and then a frequency characteristic curve (i.e., Bode diagram) of the position servo system can be obtained by performing simulation operation. The frequency sweep test is to input a sinusoidal excitation signal with constant amplitude and gradually changing frequency from low to high to the position servo system, and calculate the amplitude and the phase according to a position feedback signal and a position instruction so as to obtain the frequency characteristic of the position servo system. In this embodiment, a frequency sweep test method is used to obtain the initial frequency characteristic of the position servo system.
The debugging steps of the electromechanical servo system are as follows:
(1) the electromechanical servo system is in a unit closed loop state, and an initial frequency characteristic curve of the position servo system is obtained through a frequency sweep test by only adopting a single-proportion control algorithm, as shown in fig. 2. The ideal servo system dynamics should be: the measured amplitude characteristic curve should be below the corresponding performance index curve, and the measured phase characteristic curve should be above the corresponding performance index curve. By applying an initial frequencyThe analysis of the rate characteristic curve shows that the resonant frequency of the servo system is 10Hz, the resonant peak value is 10dB, and the index difference of the distance between the resonant frequency and the resonant peak value is not more than 4dB is obvious. The amplitude of the system has begun to rise at 3 Hz. From this, the notch center frequency ω of the second order notch filter can be determined010Hz, start frequency omega13Hz, end frequency omega2The determination principle of (2) is as follows: centered on the resonant frequency, with the starting frequency ω1Symmetrical values, i.e. omega2＝(10+7)Hz＝17Hz；
(2) According to the resonance peak value (10dB) of the position servo system, the available notch depth D must be slightly larger than the resonance peak value, and the initial notch depth D is-11 dB;
(3) according to the initial frequency omega to be corrected of the position servo system1And a termination frequency omega2An initial notch bandwidth of a quadratic notch filter may be determined
B＝|ω2-ω1|＝|17-3|＝14Hz
(4) According to the notch center frequency omega0Notch depth D, notch bandwidth B, and calculating initial molecular damping coefficient xi of initial quadratic notch filter1And denominator damping coefficient xi2
Figure GDA0003270924860000071
Figure GDA0003270924860000081
(5) According to the notch center frequency omega0Molecular damping coefficient xi1And denominator damping coefficient xi2Establishing a mathematical model of a second order notch filter
Figure GDA0003270924860000082
(6) The established notch filter is applied to an electromechanical servo system, namely the designed notch filter is subjected to discrete processing and then added to a control algorithm of a servo controller unit in the figure 2 to carry out a frequency sweep test. And obtaining a frequency characteristic curve after debugging after the sweep frequency test is finished, confirming the conformity of the frequency characteristic and the technical index, wherein the amplitude at the notch central frequency (10 Hz) is reduced from 10dB to 1dB, but the amplitude at 8Hz is slightly out of tolerance (the index requirement is not more than 3dB, and actually 3.5 dB).
(7) According to the debugging result of the step (6), the characteristic parameters of the quadratic notch filter also need to be properly adjusted. Because the resonance peak value moves forward, in order to enhance the action range of the wave trap near a wave trap frequency point, the wave trap bandwidth B can be improved and gradually increased to 21Hz, other characteristic parameters are unchanged, the steps (4), (5) and (6) are repeated, and the molecular damping coefficient xi is re-determined1Damping coefficient xi of denominator2And a mathematical model of the second order notch filter, performing a frequency sweep test, and determining a debugging result after the frequency sweep is finished, wherein the debugging result can meet the index requirement, as shown in fig. 4.
ξ1＝0.32，ξ2＝1.14
Figure GDA0003270924860000083
The electromechanical servo system in the preferred embodiment has both amplitude index and phase index, while the quadratic notch filter mainly improves the amplitude characteristic of the system, but will aggravate the phase lag, and in the actual debugging process, it needs to consider the influence degree of the method on the phase-frequency characteristic of the system, such as too deep notch depth or too wide notch bandwidth, which will increase the phase lag of the system.
In addition, since the electromechanical servo system in this example is a closed-loop system, the effect of the notch depth D cannot be fully applied to the system, and the effect is usually smaller than the notch depth actually taken, so the value of D is larger than the initial resonance peak of the system.
For the debugging of the electromechanical servo system in the embodiment, the debugging can be completed within 10 times by applying the method provided by the invention, and the molecular damping coefficient xi can be realized by adopting the traditional parameter trial and error method1Denominator resistorCoefficient xi2Factors such as difference of value deviation between the two factors in different range intervals and the like can generate great difference influence on debugging results, good regularity is not available, the debugging results can only be obtained through a large number of parameter tests, the debugging efficiency is low, uncertainty exists in the debugging process, the debugging results are estimated according to the debugging condition of a certain project at an early stage, and the debugging is usually required to be carried out for more than 500 times according to a conventional method.

Claims (2)

1. A precise debugging method based on a quadratic notch filter is characterized in that:
the method comprises the following steps:
(1) determining the trapped wave center frequency omega of the second order trapped wave filter according to the resonant frequency of the debugging object of the second order trapped wave filter and the frequency range to be corrected0Start frequency omega1End frequency omega2(ii) a Determining a trapped wave center frequency point omega of a second-order trapped wave filter according to the resonant frequency of a debugging object of the second-order trapped wave filter and a frequency range to be corrected0Start frequency omega1End frequency omega2The method is obtained by mathematical simulation or frequency sweep test;
(2) determining a notch depth D of the second-order notch filter according to a resonance peak value of a debugging object of the second-order notch filter; the influence of the notch depth D and the notch bandwidth B on the debugging object is as follows: the deeper the notch depth D is, the smaller the amplitude at the notch central frequency is, but the amplitude before the notch central frequency is raised, and the widened notch width B can improve the influence degree of the amplitude raising before the notch central frequency; in the step (2), the value of the notch depth D is below-3 dB, and the molecular damping coefficient xi1And denominator damping coefficient xi2The method is effective;
(3) according to the starting frequency omega1End frequency omega2Determining a notch bandwidth B of a quadratic notch filter; the formula is as follows:
B＝|ω2-ω1|；
(4) notching central frequency point omega according to the step (1)0Calculating the numerator of a quadratic notch filter according to the notch depth D in the step (2) and the notch bandwidth B in the step (3)Damping coefficient xi1And denominator damping coefficient xi2；
Step (4) according to the notch central frequency point omega of the step (1)0Determining the notch depth D of the step (2) and the bandwidth B of the step (3) and determining the molecular damping coefficient xi of the quadratic notch filter1The formula is as follows:
Figure FDA0003271877780000011
step (4) according to the notch central frequency point omega of the step (1)0Determining the notch depth D of the step (2) and the bandwidth B of the step (3), and determining the denominator damping coefficient xi of the quadratic notch filter2The formula is as follows:
Figure FDA0003271877780000021
(5) notching central frequency point omega according to the step (1)0And (4) the molecular damping coefficient xi of the second order notch filter of the step (4)1And denominator damping coefficient xi2Establishing a mathematical model of a second-order notch filter; the mathematical model n(s) of the quadratic notch filter of step (5) is as follows:
Figure FDA0003271877780000022
(6) debugging the frequency characteristic of the debugging object according to the mathematical model obtained in the step (5) to obtain a debugging result;
the method also comprises the step (7) of judging the debugging result of the step (6), if the debugging result is still different from the index requirement, properly adjusting the notch depth D and the notch bandwidth B according to the difference condition, repeating the steps (4), (5) and (6), establishing a new mathematical model of the second-order notch filter, and debugging again until the index requirement is met;
the debugging steps of the electromechanical servo system are as follows:
make the electromechanical servo systemThe system is in a unit closed loop state, only a single-proportion control algorithm is adopted, and an initial frequency characteristic curve of the position servo system is obtained through a frequency sweep test, wherein the ideal dynamic characteristic of the servo system is as follows: the actually measured amplitude characteristic curve is below the corresponding performance index curve, and the actually measured phase characteristic curve is above the corresponding performance index curve; by analyzing the initial frequency characteristic curve, the resonant frequency of the servo system is 10Hz, the resonant peak value is 10dB, and the index difference from the resonant peak value to the position not greater than 4dB is obvious; the amplitude of the system has begun to rise at 3 Hz; from this, the notch center frequency ω of the second order notch filter can be determined010Hz, start frequency omega13Hz, end frequency omega2The determination principle of (2) is as follows: centered on the resonant frequency, with the starting frequency ω1Symmetrical values, i.e. omega2＝(10+7)Hz＝17Hz；
According to the resonance peak value (10dB) of the position servo system, the available notch depth D must be slightly larger than the resonance peak value, and the initial notch depth D is-11 dB;
according to the initial frequency omega to be corrected of the position servo system1And a termination frequency omega2An initial notch bandwidth of a quadratic notch filter may be determined
B＝|ω2-ω1|＝|17-3|＝14Hz
According to the notch center frequency omega0Notch depth D, notch bandwidth B, and calculating initial molecular damping coefficient xi of initial quadratic notch filter1And denominator damping coefficient xi2
Figure FDA0003271877780000031
Figure FDA0003271877780000032
According to the notch center frequency omega0Molecular damping coefficient xi1And denominator damping coefficient xi2Establishing a mathematical model of a second order notch filter
Figure FDA0003271877780000033
Applying the established notch filter to an electromechanical servo system, namely adding the designed notch filter into a control algorithm of a servo controller unit after discrete processing is carried out on the designed notch filter, and carrying out a frequency sweep test; obtaining a frequency characteristic curve after debugging after the sweep frequency test is finished, confirming the conformity of the frequency characteristic and the technical index, reducing the amplitude at the notch central frequency (10 Hz) from 10dB to 1dB, but slightly exceeding the amplitude at 8Hz, wherein the index requirement is not more than 3dB, and actually 3.5 dB;
according to the debugging result, the characteristic parameters of the second-order notch filter also need to be properly adjusted; because the resonance peak value moves forward, in order to enhance the action range of the wave trap near a trap frequency point, the trap bandwidth B can be improved and gradually increased to 21Hz, other characteristic parameters are unchanged, and the molecular damping coefficient xi is redetermined1Damping coefficient xi of denominator2And a mathematical model of the second-order notch filter, performing a frequency sweep test, and determining a debugging result after the frequency sweep is finished, wherein the debugging result can meet index requirements;
ξ1＝0.32，ξ2＝1.14
Figure FDA0003271877780000041
2. an accurate debugging system based on a quadratic notch filter is characterized by comprising: the device comprises a frequency determining module, a trapped wave depth determining module, a trapped wave bandwidth determining module, a damping coefficient determining module, a modeling module and a debugging module;
a frequency determining module for determining the notch central frequency omega of the second order notch filter according to the resonant frequency of the debugging object of the second order notch filter and the frequency range to be corrected0Start frequency omega1End frequency omega2(ii) a According to a quadratic notch filterDebugging the resonant frequency and the frequency range to be corrected of the object, and determining the notch central frequency point omega of the second-order notch filter0Start frequency omega1End frequency omega2The method is obtained by mathematical simulation or frequency sweep test;
the trapped wave depth determining module is used for determining the trapped wave depth D of the second-order trapped wave filter according to the resonance peak value of the debugging object of the second-order trapped wave filter; the influence of the notch depth D and the notch bandwidth B on the debugging object is as follows: the deeper the notch depth D is, the smaller the amplitude at the notch central frequency is, but the amplitude before the notch central frequency is raised, and the widened notch width B can improve the influence degree of the amplitude raising before the notch central frequency; in the step (2), the value of the notch depth D is below-3 dB, and the molecular damping coefficient xi1And denominator damping coefficient xi2The method is effective;
a notch bandwidth determination module for determining the notch bandwidth based on the start frequency ω1End frequency omega2Determining a notch bandwidth B of a quadratic notch filter; according to the starting frequency omega1End frequency omega2Determining the bandwidth B of the quadratic notch filter, wherein the formula is as follows:
B＝|ω2-ω1|；
a damping coefficient determining module for determining the notch center frequency point omega according to the frequency0The notch depth D determined by the notch depth determining module and the notch bandwidth B determined by the notch bandwidth determining module, and calculating the molecular damping coefficient xi of the quadratic notch filter1And denominator damping coefficient xi2；
According to the notch central frequency point omega0Determining the notch depth D and the bandwidth B of the step (2) and determining the molecular damping coefficient xi of the quadratic notch filter1The formula is as follows:
Figure FDA0003271877780000051
according to the notch central frequency point omega0Determining a denominator damping coefficient xi of the quadratic notch filter according to the notch depth D and the bandwidth B of the step (3)2The formula is as follows:
Figure FDA0003271877780000052
a modeling module for determining the notch center frequency point omega according to the frequency0And the molecular damping coefficient xi of the second-order notch filter of the damping coefficient determination module1And denominator damping coefficient xi2Establishing a mathematical model of a second-order notch filter; the mathematical model of the quadratic notch filter N(s) is as follows:
Figure FDA0003271877780000053
the debugging module is used for debugging the frequency characteristic of a debugging object according to the mathematical model obtained by the modeling module to obtain a debugging result, judging the debugging result, if the debugging result has a difference with the index requirement, properly adjusting the notch depth D and the notch bandwidth B according to the difference condition, repeating the steps (4), (5) and (6), establishing a new mathematical model of the second-order notch filter, and debugging again until the index requirement is met;
the debugging steps of the electromechanical servo system are as follows:
the electromechanical servo system is in a unit closed loop state, only a single-proportion control algorithm is adopted, and an initial frequency characteristic curve of the position servo system is obtained through a frequency sweep test, wherein the ideal dynamic characteristic of the servo system is as follows: the actually measured amplitude characteristic curve is below the corresponding performance index curve, and the actually measured phase characteristic curve is above the corresponding performance index curve; by analyzing the initial frequency characteristic curve, the resonant frequency of the servo system is 10Hz, the resonant peak value is 10dB, and the index difference from the resonant peak value to the position not greater than 4dB is obvious; the amplitude of the system has begun to rise at 3 Hz; from this, the notch center frequency ω of the second order notch filter can be determined010Hz, start frequency omega13Hz, end frequency omega2The determination principle of (2) is as follows: centered on the resonant frequency, with the starting frequency ω1Symmetrical values, i.e. omega2＝(10+7)Hz＝17Hz；
According to the resonance peak value (10dB) of the position servo system, the available notch depth D must be slightly larger than the resonance peak value, and the initial notch depth D is-11 dB;
according to the initial frequency omega to be corrected of the position servo system1And a termination frequency omega2An initial notch bandwidth of a quadratic notch filter may be determined
B＝|ω2-ω1|＝|17-3|＝14Hz
According to the notch center frequency omega0Notch depth D, notch bandwidth B, and calculating initial molecular damping coefficient xi of initial quadratic notch filter1And denominator damping coefficient xi2
Figure FDA0003271877780000061
Figure FDA0003271877780000062
According to the notch center frequency omega0Molecular damping coefficient xi1And denominator damping coefficient xi2Establishing a mathematical model of a second order notch filter
Figure FDA0003271877780000063
Applying the established notch filter to an electromechanical servo system, namely adding the designed notch filter into a control algorithm of a servo controller unit after discrete processing is carried out on the designed notch filter, and carrying out a frequency sweep test; obtaining a frequency characteristic curve after debugging after the sweep frequency test is finished, confirming the conformity of the frequency characteristic and the technical index, reducing the amplitude at the notch central frequency (10 Hz) from 10dB to 1dB, but slightly exceeding the amplitude at 8Hz, wherein the index requirement is not more than 3dB, and actually 3.5 dB;
according to the debugging result, alsoThe characteristic parameters of the quadratic notch filter need to be properly adjusted; because the resonance peak value moves forward, in order to enhance the action range of the wave trap near a trap frequency point, the trap bandwidth B can be improved and gradually increased to 21Hz, other characteristic parameters are unchanged, and the molecular damping coefficient xi is redetermined1Damping coefficient xi of denominator2And a mathematical model of the second-order notch filter, performing a frequency sweep test, and determining a debugging result after the frequency sweep is finished, wherein the debugging result can meet index requirements;
ξ1＝0.32，ξ2＝1.14
Figure FDA0003271877780000071
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